Converting 3/8 to a Decimal

Pre-Algebra · Axiom Academy

EXAMPLE Converting 3/8 to a Decimal Use long division to convert to decimal form, and see what makes a decimal terminate versus repeat. Convert the fraction to a decimal using long division. Then classify the result as a terminating or repeating decimal. Terminating vs. Repeating Decimals Here is a side-by-side of what this example showed: • Ends after a finite number of digits • The remainder becomes 0 in long division • Denominator (in lowest terms) has only factors of 2 and 5 • Digits repeat in a pattern forever • The same remainder appears again in the division • Use bar notation to mark the repeating block Nice work. You converted a fraction to a decimal with long division and learned to tell terminating from repeating decimals. Long-division method: divide the numerator by the denominator, appending zeros as needed. Terminating decimals: end after a finite number of digits (like ). Repeating decimals: have digits that repeat in a pattern (like ). Bar notation: a bar over the digits marks the part that repeats forever ( ). Quick check: if the denominator in lowest terms has only factors of 2 and 5, the decimal terminates. Practice tip: try converting , , and . Can you predict which terminate and which repeat before you start?

This is the written version of the interactive lesson above. See the full Pre-Algebra course.